An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... Conic Sec- tion · • · 2 , 3. Equation of the Conic described about the Triangle of Refer- 33333 ence 34 · · • 4 . Position of the Centre . Condition for a Parabola 35 5 . Condition of Tangency . Every Parabola touches the Line at ...
... Conic Sec- tion · • · 2 , 3. Equation of the Conic described about the Triangle of Refer- 33333 ence 34 · · • 4 . Position of the Centre . Condition for a Parabola 35 5 . Condition of Tangency . Every Parabola touches the Line at ...
Page ix
... CONIC REPRESENTED BY THE GENERAL EQUATION OF THE 2 . SECOND DEGREE . To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the conic again · Equation of the Tangent at a given ...
... CONIC REPRESENTED BY THE GENERAL EQUATION OF THE 2 . SECOND DEGREE . To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the conic again · Equation of the Tangent at a given ...
Page x
... conic is a conic 8 . The degree of a curve is the same as the class of its reciprocal , Equation of the Polar Reciprocal of one Conic with regard to 106 · 107 another ib . 10 . Instances of Transformation 109 · 12 . Brianchon's Theorem ...
... conic is a conic 8 . The degree of a curve is the same as the class of its reciprocal , Equation of the Polar Reciprocal of one Conic with regard to 106 · 107 another ib . 10 . Instances of Transformation 109 · 12 . Brianchon's Theorem ...
Page xi
... Conic . 126 · 34 . Double application of the Method of Reciprocal Polars EXAMPLES 128 • ib , CHAPTER VII . 2 , 3 . 4 ... Conic , touching the three sides of the triangle of reference ib . 8 . Equation of circumscribed Conic 138 · 9 ...
... Conic . 126 · 34 . Double application of the Method of Reciprocal Polars EXAMPLES 128 • ib , CHAPTER VII . 2 , 3 . 4 ... Conic , touching the three sides of the triangle of reference ib . 8 . Equation of circumscribed Conic 138 · 9 ...
Page xii
... conics may be projected into hyperbolas of any assigned eccentricity ib . ib . 19 . 20 . • 21 . 22 . • Any two conics may be projected into conics of any eccentricity , or into circles : Projection of the foci and directrices of a Conic ...
... conics may be projected into hyperbolas of any assigned eccentricity ib . ib . 19 . 20 . • 21 . 22 . • Any two conics may be projected into conics of any eccentricity , or into circles : Projection of the foci and directrices of a Conic ...
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Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα